STUDY ON THE LOCAL FRACTIONAL (3+1)-DIMENSIONAL MODIFIED ZAKHAROV–KUZNETSOV EQUATION BY A SIMPLE APPROACH

Abstract

Under the current research, the local fractional (3+1)-dimensional modified Zakharov–Kuznetsov equation (MZKE) is explored. With the Mittag–Leffler function (MLF) defined on the Cantor sets (CS), four special functions, namely the [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] are extracted to construct an auxiliary function. Then the auxiliary function, along with Yang’s non-differentiable (ND) transformation, is manipulated to explore the ND exact solutions (ESs). By means of the proposed method, four different sets of the ND ESs are found in just one step. The nonlinear dynamics of the ND exact solutions on the CS are illustrated graphically. Furthermore, the ND exact solutions for [Formula: see text] and the classic exact solutions for [Formula: see text] are also compared and discussed in detail via the 2-D curves. The attained results reveal that the method is a simple but effective tool to deal with local fractional PDEs arising in physics and maths.